With fewer emissions, higher efficiency, and quicker response than traditional coal-fired thermal power plants, the combined-cycle units (CCUs), as gas-fired generators, have been increasingly adapted in the U.S. power system to enhance the smart grids operations. Meanwhile, due to the inherent uncertainties in the deregulated electricity market, e.g., intermittent renewable energy output, unexpected outages of generators and transmissions, and fluctuating electricity demands, the electricity price is volatile. As a result, this brings challenges for an independent power producer (served in the self-scheduling mode) owning CCUs to maximize the total profit when facing the significant price uncertainties. In this paper, a data-driven risk-averse stochastic self-scheduling approach is presented for the CCUs that participate in the real-time market. The proposed approach does not require the specific distribution of the uncertain real-time price. Instead, a confidence set for the unknown distribution is constructed based on the historical data. The conservatism of the proposed approach is adjustable based on the amount of available data. Finally, numerical studies show the effectiveness of the proposed approach.